Parasite‐mediated selection on host phenology

Abstract The timing of seasonal activity, or phenology, is an adaptive trait that maximizes individual fitness by timing key life events to coincide with favorable abiotic factors and biotic interactions. Studies on the biotic interactions that determine optimal phenology have focused on temporal overlaps among positively‐interacting species such as mutualisms. Less well understood is the extent that negative interactions such as parasitism impact the evolution of host phenology. Here, we present a mathematical model demonstrating the evolution of host phenological patterns in response to sterilizing parasites. Environments with parasites favor hosts with shortened activity periods or greater distributions in emergence timing, both of which reduce the temporal overlap between hosts and parasites and thus reduce infection risk. Although host populations with these altered phenological patterns are less likely to mature and reproduce, the fitness advantage of parasite avoidance can be greater than the cost of reduced reproduction. These results illustrate the impact of parasitism on the evolution of host phenology and suggest that shifts in host phenology could serve as a strategy to mitigate the risk of infection.


| INTRODUC TI ON
The timing of seasonal activity, or phenology, is an adaptive trait that maximizes individual fitness by timing key life events within a season. The phenological pattern that maximizes individual fitness is impacted by many abiotic environmental factors that determine when activities such as breeding, foraging, and migration are favorable (Forrest & Miller-Rushing, 2010). Similarly, biotic factors such as inter-species interactions impact phenology by selecting seasonal activity patterns that overlap temporally with food sources and mutualists (e.g., plants and pollinators) (Elzinga et al., 2007;Kochmer & Handel, 1986;Sargent & Ackerly, 2008). The multitude of seasonally varying abiotic and biotic factors preclude most species from optimizing their phenological pattern to each factor simultaneously (Pau et al., 2011;Van Schaik et al., 1993). For example, plants must balance the costs of herbivory with the benefits of pollination as the seasonal activity of insect herbivores and pollinators often overlap (Van Schaik et al., 1993). Although many abiotic and biotic factors that impact phenology have been investigated, the impacts of parasitism remain relatively under-explored.
Parasites are an important driver of the evolution of many phenotypes. For example, nearly all species have evolved energetically costly defenses against infection including innate and adaptive immune responses (Rimer et al., 2014). Parasite-induced shifts in host phenology could serve as an alternative defense against infection, although it is unclear whether the benefits associated with reducing infection risks caused by phenological shifts would surpass the opportunity costs incurred due to missing other seasonal events (e.g., reproduction and development time) (Alexander et al., 1993;Biere & Antonovics, 1996). Nevertheless, there are several examples in which certain host phenological patterns are correlated with a decrease in infection risk. For example, late-flowering Silene alba have lower infection rates with the sterilizing anther-smut fungus (Ustilago violacea) than early-flowering plants (Alexander, 1989(Alexander, , 1990Biere & Antonovics, 1996;Biere & Honders, 1996). Late-flowering plants do, however, have lower flower production, a measure of plant reproductive fitness (Biere & Antonovics, 1996;Biere & Honders, 1996).
Changes in host phenology could reduce infection rates in multiple ways. For example, host activity patterns that do not temporally overlap with the peak in parasite abundance directly decrease infection risk. This mechanism is supported empirically in several systems. Namely, temporal coordination between hosts and parasites is a major determinant of trematode infections of the amphibian Pseudacris regilla, parasitic wasp infections in apple maggot flies, and nematode infections in sheep (Feder, 1995;Gethings et al., 2015;McDevitt-Galles et al., 2020). Host phenological patterns could also be suboptimal for parasite fitness resulting in ecological feedback that reduces host infection risks in future years. Although host phenological patterns likely impact infection risk, few studies have focused on how host phenological patterns could have arisen through selection to decrease infection risk.
We develop a mathematical model to assess the impact of parasitism on the evolution of host phenology. Specifically, the model evaluates the fitness advantages of avoiding infection through alternate host activity patterns along with the potential fitness costs incurred. In this model, the fitness of hosts emerging later is lower due to reduced reproductive potential, but these hosts also have lower risks of sterilizing infections. Given the assumptions of the model, late-shifted host phenological patterns can be an adaptive strategy resulting in greater individual fitness and population densities in environments with parasites. That is, the presence of parasites can select for late-shifted host phenological patterns and an increased duration in the host emergence period even though both phenological changes reduce the reproductive potential of individual hosts. This study demonstrates that parasitism can impact the evolution of host phenology and provides a framework for predicting the impact of future changes in parasite abundance on host species.

| MODEL DE SCRIP TION
The model describes the transmission dynamics of a free-living, sterilizing parasite that infects seasonally available juvenile hosts ( Figure 1). The susceptible host cohort, ŝ(n), enters the system as juveniles at the beginning of season n. The timing of juvenile host emergence during the season, that is, host phenology, is given by the function g t 0 , t l , which describes when host emergence begins (at t = t 0 ) and the length of time over which ŝ(n) emerge (t l ). Hosts have nonoverlapping generations and are alive for one season. The parasite, v n , infects juvenile hosts, s n , who are susceptible to infection, analogous to, for example, baculoviruses of forest Lepidoptera (Baltensweiler et al., 1977;Bilimoria, 1991;Dwyer, 1994;Dwyer & Elkinton, 1993;Woods & Elkinton, 1987) and univoltine insects parasitized by ichneumonids (Campbell, 1975;Delucchi, 1982;Kenis & Hilszczanski, 2007). The parasite releases new infectious progeny only after a set latency period ( ), which determines the number of rounds of infection the parasite completes within a season. The parasite completes one round of infection per season if the parasite has F I G U R E 1 Diagrammatic representation of host infection and maturation within each season. Juvenile hosts (s) emerge at a constant rate between time t = t 0 and t = t 0 + t l and develop into adult hosts (a) at rate l . Only hosts that have matured by the end of the season contribute progeny that will emerge in the next season. All parasites (v) emerge at the beginning of the season (t = 0). The rate of infection is densitydependent such that the majority of the first round of infections occur near the beginning of the season when susceptible host and free parasite densities are high. New parasites are released at time postinfection. If is short enough, more than one generation of infections can occur within the season. Parasite progeny that survive in the environment to the end of the season comprise the parasite population that emerges in the following season. a long latency period (long ) while the parasite completes multiple rounds of infection per season if the parasite has a short latency period (short ). Juvenile hosts mature into the adult developmental stage, a n , that is resistant to infection during the season. Adult hosts reproduce in between-seasons to give rise to next season's host cohort (ŝ(n + 1)). We assume infected s n hosts cannot reproduce and thus ignore their progression to the reproductively active a n stage.
The duration of each season extends from t = 0 to t = T. Time units are not specified in order to maintain the generality of the model across disease systems. It is expected that the relevant time unit will be in months for many disease systems, corresponding to spring and summer (Baltensweiler et al., 1977;Danks, 2006;Donovan, 1991;Grant & Shepard, 1984;Takasuka & Tanaka, 2013) and weeks for other disease systems (Cummins et al., 2011;Dalen, 2013;Danks, 2006). The initial conditions in the beginning of the season are is the size of the starting parasite population introduced at the beginning of season n, which is the product of the number of parasites progeny remaining at the end of season (t = T) in season n − 1 and the probability that those parasites survive between-seasons ( ). The transmission dynamics in season n are given by the following system of delay differential equations (all parameters are described in Table 1): where is the host death rate, l is the host maturation rate, is the decay rate of parasites in the environment, is the density-dependent transmission rate, and is the delay between host infection and host death. The term e − s is the proportion of infected hosts who survive the latency period. is the number of parasites released upon host death at the end of the latency period ( ). We make the common assumption for free-living parasites that the removal of parasites through transmission ( ) is negligible (Anderson & May, 1981;Caraco & Wang, 2008;Dwyer, 1994), that is, (1c) ignores the term − s n (t)v n (t) .
The function g t 0 , t l is a probability density function that captures the per-capita host emergence rate by specifying the timing and length of host emergence. We use a uniform distribution (U ( • ) ) for simplicity, although other distributions are expected to have qualitatively similar results (MacDonald et al., 2022). t 0 denotes the start of first host emergence, t l denotes the length of the host emergence period, and T denotes the season length. The host cohort emerges from t 0 ≤ t ≤ t 0 + t l . ŝ(n) is a function of the density of mature hosts that survive to the end of the previous season (a n−1 (T)), given by where ϵ is the probability that hosts survive to the next season, is host reproduction, and is the density-dependent parameter.
Infections that have not completed the full latency period ( ) by the end of the season do not release progeny. Background mortality arises from predation or some other natural cause. We assume that infected hosts that die from background mortality do not release parasites because the parasites are either consumed or the latency period corresponds to the time necessary to develop viable progeny (Wang, 2006;White, 2011).
In previous work on a similar model, we derived an analytical expression for end-of-season host and parasite density (a n (T), v n (T), respectively) (MacDonald & Brisson, 2022a). However, we can only solve system (1) in the current framework analytically if is long enough that parasites only complete one infection generation per season. We outline the analysis for this case in Appendix S1A. All other results were found by performing numerical computations.
We have shown previously that host carryover can generate a feedback between parasite fitness and host demography that drives quasiperiodic dynamics for some parameter ranges (MacDonald & Brisson, 2022a, 2022b. In this study, we found no evidence that host-parasite cycling occurs for the parameter ranges considered, that is, the dynamics always eventually settle to stable end-ofseason densities.

| Host evolution
To study how host phenology traits adapt when challenged by parasites, we use evolutionary invasion analysis (Geritz et al., 1998;Metz et al., 1992). We first extend system (1) to follow the invasion dynamics of a rare mutant host where m subscripts refer to the invading mutant host and its corresponding traits.
To estimate the invasion fitness of a single mutant, we define mutant invasion fitness as the density of s n+1,m emerging in season n + 1 (ŝ m (n + 1)) produced by a single invading mutant host (ŝ m (n) = s n,m (0) = 1) introduced in season n in the environment set by the resident host at equilibrium density ŝ * . That is, mutant invasion fitness is equivalent to ŝ m (n + 1) that were produced in season n by s n,m who successfully matured by the end of the season a n,m (T) .
Following the same approach as in previous analyses (MacDonald et al., 2022;MacDonald & Brisson, 2022a, 2022b, the mutant host invades in a given host phenological scenario if ŝ m (n + 1) is greater than or equal to the initial ŝ m (n) = s n,m (0) = 1 introduced at the start of season n ŝ m (n + 1) ≥ 1 . Optimal phenological traits (t * 0 , t * l ) are those that invade and replace populations with alternative trait values when rare and also prevent invasion, while at equilibrium, from mutants with different trait values. We are only able to solve the current model analytically when hosts are challenged by parasites that complete one round of infection per season (Appendix S1B). For consistency, we determine all host evolutionary endpoints numerically (Appendix S1C.) The invasion analyses predict the evolution of the timing that host emergence begins (t 0 ) and the host emergence period duration (t l ) when hosts are in an environment with a parasite with a defined latency period length. Optimal trait values for t 0 and t l thus balance the cost of parasite infection with the cost of not reproducing. This study followed the evolution of t 0 or t l in isolation, rather than the simultaneous evolution of both traits. Parameter values are listed in Table 1.

| RE SULTS
Host emergence near the beginning of the season maximizes the probability of maturing and producing offspring ( Figure 2). By contrast, later-emerging hosts are less likely to reach reproductive maturity due to their shorter activity period. The costs associated with reducing the probability of reaching reproductive maturity, however, can be less than the costs associated with the risk of parasitic infection, which are greatest in early-emerging hosts.
That is, hosts that emerge early are at higher risk of infection from the sterilizing parasites that are most abundant at the beginning of the season and subsequently decay. Thus, the presence of parasites can create a selective pressure favoring later host emergence despite the cost of reducing the probability of reaching reproductive maturity.
Shifts in the start of the activity period can increase host reproductive fitness through increased host density both directly and indirectly (Figure 3). Shifting the start of the activity period later in , calculated using equation 3) for combinations of the timing at which hosts first emerge (t 0 ) and the length of the host emergence period (t l ). Note the when t 0 + t l > T, not all hosts emerge before the end of the season. = 2, n = 100, all other parameters are the same as in Table 1. Note that legends are at different scales.

(a) (b)
F I G U R E 3 Late-shifted phenological activity patterns maximize host density in environments with parasites. Top row: equilibrium host density (i.e., the size of the host cohort calculated using equation 3) is higher in environments without parasites (ŝ * = 5.08 * 10 6 ) compared with environments with parasites (ŝ * = 4.94 * 10 6 ) when t 0 = 0, t l = 0.5. Early phenology grants high host density in the absence of parasites but results in most hosts becoming infected in environments with parasites as parasite density is high early in the season. Middle row: host populations that begin emerging late in environments with parasites increase their density compared with populations that emerge at t = 0 by avoiding high parasite densities early in the season and effectively eliminating infections (ŝ * = 5.08 * 10 6 , t 0 = 0.91). Host population density is the same regardless of whether parasites are introduced when t 0 = 0.91 as the host phenological pattern does not support parasites. Bottom row: host populations with longer emergence periods (t l = 2.88) also increase their density compared to populations with shorter emergence periods (t l = 0.5) as hosts that emerge late in the cohort avoid high early season parasite densities (ŝ * = 5.02 * 10 6 when t l = 2.88). However, longer emergence periods do not drive parasites extinct, thus gains in host density do not fully recover losses in host density due to parasitism (ŝ * = 5.08 * 10 6 , t l = 2.88 in environments without parasites.) Gray line: first generation of parasites in the season, black line: infected hosts, dashed black line: mature hosts. = 3, n = 150 (population dynamics reached stable end-of-season densities), all other parameters are the same as in Table 1.

F I G U R E 4
Late emergence starts are adaptive for host species in environments with parasites with short latency periods (short ) by reducing host infection prevalence. (a) A later emergence start (t * 0 = 2.13) is adaptive in environments with parasites that have short latency periods ( = 1.5 ) as infection risk is essentially eliminated (host infection prevalence is close to 0). (b) Only a slightly later emergence start (t * 0 = 0.91) is necessary to eliminate infections from long latency period parasites ( = 3). t 0 is the time within the season that host emergence begins (i.e., emergence begins at t = t 0 ). Dots correspond to the optimal emergence start (t * 0 ) when parasites have short latency (a) and long latency (b). n = 300, in the absence of parasites, t * 0 = 0, all other parameters are the same as in Table 1. These results suggest that, for example, late-flowering phenology in Silene alba could be an adaptation to avoid Ustilago violacea infection (Alexander, 1989;Biere & Antonovics, 1996;Biere & Honders, 1996). Further, evolutionary increases in host emergence period duration are a less-effective means of decreasing infection risk than evolutionary changes in the timing of first emergence. Interestingly, long host emergence periods can also serve as a bet-hedging strategy in response to temporally variable environments (Simons, 2014) such that the benefits of bet-hedging could come at the cost of increased infection risk.
The host phenological traits under selection in this study (emergence start and period length) could represent several activity types that impact host contact with parasites in natural systems. For example, this model could apply to host species that undergo diapause during unfavorable environmental conditions, as in many disease systems with insect hosts (Delucchi, 1982;Donovan, 1991;Grant & Shepard, 1984;Takasuka & Tanaka, 2013). Similarly, host phenology could represent the start and length of time that host species are born (Campbell, 1975;Danks, 2006;Kenis & Hilszczanski, 2007).
These results could also apply to disease systems with hosts that migrate to the same area each season, with emergence start and emergence period length representing the start and length of time over which hosts migrate into an area, respectively. Theory developed on the evolution of host migration has some parallels to the F I G U R E 5 Long emergence period lengths are adaptive for host species in environments with parasites with long latency periods (long ) but do not eliminate infection risk as measured by host infection prevalence. (a) A slightly longer emergence period length (t * l = 1.45) is adaptive in environments with parasites that have short latency periods ( = 1.5). (b) A long emergence period (t * l = 2.88) is adaptive in environments with parasites that have long latency periods ( = 3) to decrease the risk of infection. t l is the length of the host emergence period. Dots correspond to the optimal emergence period length (t * l ) when parasites have short latency (a) and long latency (b). n = 300 , in the absence of parasites, t * l = 0.5 (minimum possible emergence period length), all other parameters are the same as in Table 1. results presented herein that host-parasite intensity is predicted to select for partial host migration (Balstad et al., 2021;Shaw & Binning, 2016)-a prediction that is matched by empirical data on reindeer (Folstad et al., 1991) and fish migration (Poulin et al., 2012;Sikkel et al., 2017).
The presented model assumes that host phenology can evolve in response to parasite infection risks without considering parasite evolution. This strict assumption, which likely impacts long-term dynamic and equilibrial results, is unlikely to occur in any natural system. For example, phenological evolution in apple maggot fly populations driven by parasitic wasps is followed by the phenological evolution of wasp species (Feder, 1995;Hood et al., 2015). Similarly, parameter ranges that increase infections would likely select for stronger shifts in host phenology (e.g., larger numbers of parasites produced upon host death, lower parasite decay rates) while parameter ranges that decrease the density of susceptible hosts would likely select for weaker shifts in host phenology by decreasing the number of infections (e.g., increased host death and maturation rates.) We explore the impact of changing transmission rates ( ), host fecundity ( ), and the strength of the host density-dependent parameter ( ) in Appendix S1D. We find that the host density-dependent parameter strongly impacts optimal host phenology while only extremely small transmission rates and extremely small host fecundity values select for smaller shifts in host phenology. Future work will consider these extensions in more detail to move toward the goal of developing a more complete theory on the role infection can play in host adaptation in seasonal environments.
Parasites are important drivers of host evolution through their impact on host fitness. While the majority of research on the impacts of parasites on hosts focuses on the evolution of immune defenses, the current study presents an alternative evolutionary mechanism in the form of altered seasonal patterns to reduce infection risk. The theory developed here predicts that parasitism can drive host phenology evolution, providing a framework to determine how future changes in parasite distribution and abundance could impact host evolution.

FU N D I N G I N FO R M ATI O N
This work was supported by the National Institutes of Health (T32AI141393 (HM) R01AI142572 (DB), R01AI097137 (DB)); the National Science Foundation (DEB-1354184 (DB)); and the Burroughs Wellcome Fund (1012376 (DB)).

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors declare no conflicts of interest.

This article has earned Open Data, Open Materials and Preregistered
Research Design badges. Data, materials and the preregistered design and analysis plan are available at [https://github.com/hanne lorem ac/Paras ite-media ted-selec tion-on-host-pheno logy].

DATA AVA I L A B I L I T Y S TAT E M E N T
Code is available on the Github repository: https://github.com/ hanne lorem ac/Paras ite-media ted-selec tion-on-host-pheno logy.

PE R M I SS I O N TO R E PRO D U CE M ATE R I A L S FRO M OTH E R S O U RCE S
None.

S U PP O RTI N G I N FO R M ATI O N
Additional supporting information can be found online in the Supporting Information section at the end of this article.